Electric power is ordinarily delivered to residences, commercial facilities, and industrial facilities as an alternating current (AC) voltage that approximates a sine wave with respect to time. The electric power ordinarily flows through a residence or facility as an AC current that also approximates a sine wave with respect to time.
The electric power distribution system operates most efficiently and most safely when both the voltage and current are sine waves. However, certain kinds of loads draw current in a non-sinusoidal waveform. If these loads are large relative to the distribution system source impedance, the system voltage will become non-sinusoidal as well.
These non-sinusoidal voltage and current waveforms may be conveniently expressed as a Fourier series (a sum of sinusoidal waveforms of differing frequencies, magnitudes, and phase angles). Under most circumstances, the Fourier series for AC power system voltage and currents consists of a fundamental frequency, typically 50 Hertz or 60 Hertz, plus integer multiples of the fundamental frequency. These integer multiples of the fundamental frequency are referred to as "harmonics".
In AC power system measurements, it is a well-known technique to sample, at regular intervals much shorter than one period of the fundamental waveform, a voltage or current waveform for a length of time called a "sampling window", then convert those samples to digital values yielding a digital discrete time-domain representation of the waveform. It is also a well-known technique to employ a Discrete Fourier Transform (DFT) or a Fast Fourier Transform (FFT), which is a special case of the DFT, to convert that time-domain representation of the waveform to a frequency-domain representation. This frequency-domain representation can be used to measure the magnitude and phase angle of the harmonics present in an AC power system voltage or current waveform.
It is known to those familiar with the art that calculation of a frequency-domain representation of an AC power system waveform from a time-domain representation can require substantial computing power. In particular, where there are N samples in the time-domain representation, the number of complex multiplications in a Discrete Fourier Transform is proportional to N.sup.2 and the number of complex multiplications in a Fast Fourier Transform is proportional to N log N.
It is an object of the present invention to reduce the number of calculations required to produce a frequency-domain representation of AC power system voltage and current measurements.